Question

Ten years ago 53% of American families owned stocks or stock funds. Sample data collected by the Investment Company Institute indicate that the percentage is now 44%. (a) Choose the appropriate hypotheses such that rejection of H0 will support the conclusion that a smaller proportion of American families own stocks or stock funds this year than 10 years ago. H0: p Ha: p (b) Assume the Investment Company Institute sampled 300 American families to estimate that the percent owning stocks or stock funds is 44% this year. What is the p value for your hypothesis test? If required, round your answer to four decimal places. Do not round your intermediate calculations. (c) At α = 0.01, what is your conclusion? We the null hypothesis. We conclude that a smaller proportion of American families own stocks or stock funds this year than they did 10 years ago.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.53

H_a : p < 0.53

n = 300

= 0.44

P₀ = 0.53

1 - P₀ = 1 - 0.53 = 0.47

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.44 - 0.53 / [(0.53 * 0.47) / 300]

= -2.43

Test statistic = -2.43

P(z < -2.43) = 0.0075

P-value = 0.0075

= 0.01

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that the smaller proportion of American families own stocks or stock funds this year than they did 10 years ago .